Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

Some remarks concerning the Fourier transform in the space L2(ℝn)

Abstract: Two useful estimates are proved for the Fourier transform in the space of square integrable functions on certain classes of functions characterized by the generalized continuity modulus.

A fast modified sine transform for solving block-tridiagonal systems with Toeplitz blocks

Abstract: In this report we consider block-tridiagonal systems with Toeplitz blocks. Each block is of sizen×n consisting ofn c×n c matrices as entries, and there arem×m blocks in the system. The solution of those systems consists of 2n c m modified sine transforms and an intermediate solution ofn block-tridiagonal systems. Symmetries in the data vectors are exploited such that one modified sine transform can be computed in terms of one Fourier transform of half the length of the original one, hence requiringO(2.5nlog2 n) operations. Similarly, we only have to solve (n+1)/2 of the intermediate systems due to symmetry.

Prime factor FFT algorithms for real-valued series

Abstract: This paper presents two techniques for computing a discrete transform of a vector of real-valued data using the Prime Factor Algorithm (PFA) with high-speed convolution. These techniques are applied to the Discrete Fourier Transform (DFT) and the Discrete Hartley Transform (DHT). The primary goals of these techniques are to eliminate unnecessary computations required when implementing a complex transform on a real-valued vector, to compute the transform in-place in the original length-N real vector, and to obtain the transform coefficients in-order. The two algorithms described require modification of the Winograd short-length transform modules to accommodate a real input. One technique replaces the modules in the Burrus-Eschenbacher PFA program with the modified real-input modules and constructs the complete transform in a final step of additions and subtractions after modules for each factor have been executed. The other technique uses these real-input DFT modules for part of the computation associated with each factor and requires complex input DFT modules for another part of the computation. These algorithms require exactly one half of the number of multiplications and slightly less than one half of the number of additions required by a complex-input PFA.

Theorems on L 2 -transform and its applications

Abstract: In the present paper the author proves Parseval-Goldstein-type theorems involving a Laplace-type integral tranform, the Widder transform and the K-transform. The theorem is then shown to yield a number of new identities involving several well-known integral transforms. Using the theorems and its corollaries, a number of interesting infinite integrals of elementary and special functions are presented. Some illustrative examples are also given.

Fractional Radon transform: definition.

Abstract: In this paper a novel fractional transformation for which we coin the term the fractional Radon transform is defined. This transform generalizes the Radon transform and combines it with the fractional Fourier transform. Both transformations are useful tools for invariant pattern recognition, tomography, and signal processing. Some of the properties of the new transformation, as well as further directions for investigation, are presented.